Well-posedness and long time behavior for p-Laplacian equation with nonlinear boundary condition

Antontsev, Stanislav; ÖZTÜRK, EYLEM

doi:10.1016/j.jmaa.2018.12.011

Well-posedness and long time behavior for p-Laplacian equation with nonlinear boundary condition

Atıf İçin Kopyala

Antontsev S., ÖZTÜRK E.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.472, sa.2, ss.1604-1630, 2019 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 472 Sayı: 2
Basım Tarihi: 2019
Doi Numarası: 10.1016/j.jmaa.2018.12.011
Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.1604-1630
Hacettepe Üniversitesi Adresli: Evet

Özet

In this paper, we study the homogeneous nonlinear boundary value problem for the p-Laplacian equation u(t) - Delta(u)(p) + a(x, t)vertical bar u vertical bar(sigma-2)u - b(x,t)vertical bar u vertical bar(v-2)u = h(x, t). We prove the existence of weak solutions which is global or local in time in dependence on the relation between the exponent of nonlinear part in boundary value and p. Boundedness of weak solution is proved. We established conditions of uniqueness. We prove also the properties of extinction in a finite time, finite speed propagation and waiting time. Lastly, by using the energy method, we obtain sufficient conditions that the solutions of this problem with non-positive initial energy blow up in finite time. (C) 2018 Elsevier Inc. All rights reserved.